Dalitz plot analysis of the decay <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>ω</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>

Using a low-background sample of $2.6\ifmmode\times\else\texttimes\fi{}{10}^{5}\text{ }\text{ }J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\eta}(\ensuremath{\omega}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0},\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma})$ events, about 5 times larger statistics than previous experiments, we present a Dalitz plot analysis of the decay $\ensuremath{\omega}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$. It is found that the Dalitz plot distribution differs from the pure $P$-wave phase space with a statistical significance of $18.9\ensuremath{\sigma}$. The parameters from the fit to data are in reasonable agreement with those without the cross-channel effect within the dispersive framework, which indicates that the cross-channel effect in $\ensuremath{\omega}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ is not significant.